Nuprl Lemma : cut-order-prior
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:sys-antecedent(es;X)]. ∀[a:E(X)].
prior(X)(a) ≤(X;f) a supposing ↑a ∈b prior(X)
Proof
Definitions occuring in Statement :
cut-order: a ≤(X;f) b,
es-prior-interface: prior(X),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type
Definitions unfolded in proof :
top: Top,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
sys-antecedent: sys-antecedent(es;Sys),
subtype_rel: A ⊆r B,
prop: ℙ,
cand: A c∧ B,
or: P ∨ Q,
guard: {T},
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
es-E-interface: E(X),
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:sys-antecedent(es;X)]. \mforall{}[a:E(X)].
prior(X)(a) \mleq{}(X;f) a supposing \muparrow{}a \mmember{}\msubb{} prior(X)
Date html generated:
2016_05_17-AM-07_43_08
Last ObjectModification:
2015_12_28-PM-11_34_46
Theory : event-ordering
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